Local null controllability of the two-dimensional Navier-Stokes system in the torus with a control force having a vanishing component

被引：23

作者：

Coron, Jean-Michel ^{[1
,2
]}

Guerrero, Sergio ^{[2
]}

机构：

[1] Inst Univ France, F-75005 Paris, France

[2] Univ Paris 06, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2009年 / 92卷 / 05期

关键词：

Navier-Stokes system; Controllability; Return method; EXACT BOUNDARY CONTROLLABILITY; INCOMPRESSIBLE PERFECT FLUIDS; BURGERS-TYPE EQUATIONS; N-1 SCALAR CONTROLS; APPROXIMATE CONTROLLABILITY; GLOBAL-CONTROLLABILITY;

D O I：

10.1016/j.matpur.2009.05.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we deal with the two-dimensional Navier-Stokes system in a torus. The main result establishes the local null controllability with internal controls having one vanishing component. The linearized control system around 0 is not null controllable: the nonlinear term is essential to get this null controllability. Our proof uses the return method together with previous results by Fursikov and Imanuvilov. (C) 2009 Elsevier Masson SAS. All rights reserved.

引用

页码：528 / 545

页数：18

共 26 条

[1] Navier-Stokes equations: Controllability by means of low modes forcing [J].